*The author of this computation has been verified*

R Software Module: /rwasp_arimaforecasting.wasp (opens new window with default values)

Title produced by software: ARIMA Forecasting

Date of computation: Wed, 09 Dec 2009 05:10:54 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/09/t1260360819mkpgu5bh228lu4f.htm/, Retrieved Wed, 09 Dec 2009 13:13:41 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/09/t1260360819mkpgu5bh228lu4f.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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117,09 116,77 119,39 122,49 124,08 118,29 112,94 113,79 114,43 118,70 120,36 118,27 118,34 117,82 117,65 118,18 121,02 124,78 131,16 130,14 131,75 134,73 135,35 140,32 136,35 131,60 128,90 133,89 138,25 146,23 144,76 149,30 156,80 159,08 165,12 163,14 153,43 151,01 154,72 154,58 155,63 161,67 163,51 162,91 164,80 164,98 154,54 148,60 149,19 150,61

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Univariate ARIMA Extrapolation Forecast time Y[t] F[t] 95% LB 95% UB p-value (H0: Y[t] = F[t]) P(F[t]>Y[t-1]) P(F[t]>Y[t-s]) P(F[t]>Y[22]) 10 118.7 - - - - - - - 11 120.36 - - - - - - - 12 118.27 - - - - - - - 13 118.34 - - - - - - - 14 117.82 - - - - - - - 15 117.65 - - - - - - - 16 118.18 - - - - - - - 17 121.02 - - - - - - - 18 124.78 - - - - - - - 19 131.16 - - - - - - - 20 130.14 - - - - - - - 21 131.75 - - - - - - - 22 134.73 - - - - - - - 23 135.35 136.1297 131.4926 140.7667 0.3709 0.7229 1 0.7229 24 140.32 138.478 130.0959 146.8602 0.3333 0.7677 1 0.8096 25 136.35 137.4139 125.849 148.9789 0.4285 0.3112 0.9994 0.6754 26 131.6 135.8198 121.8706 149.769 0.2766 0.4703 0.9943 0.5608 27 128.9 135.5665 120.3442 150.7889 0.1953 0.6952 0.9895 0.5429 28 133.89 137.0117 120.5858 153.4376 0.3548 0.8335 0.9877 0.6073 29 138.25 137.5551 119.6669 155.4433 0.4697 0.656 0.965 0.6215 30 146.23 136.8082 117.337 156.2795 0.1715 0.4423 0.887 0.5829 31 144.76 135.9862 115.2921 156.6802 0.203 0.166 0.6762 0.5474 32 149.3 136.3156 114.6471 157.9842 0.1201 0.2225 0.7118 0.557 33 156.8 137.0262 114.3707 159.6818 0.0436 0.1442 0.676 0.5787 34 159.08 137.0891 113.3125 160.8657 0.0349 0.0521 0.5771 0.5771 35 165.12 136.5389 111.6809 161.3969 0.0121 0.0378 0.5373 0.5567 36 163.14 136.2924 110.5105 162.0744 0.0206 0.0142 0.3797 0.5473 37 153.43 136.6072 109.9879 163.2264 0.1077 0.0254 0.5076 0.555 38 151.01 136.9304 109.4378 164.423 0.1577 0.1197 0.648 0.5623 39 154.72 136.8082 108.4066 165.2097 0.1082 0.1635 0.7074 0.557 40 154.58 136.5151 107.2534 165.7768 0.1131 0.1113 0.5698 0.5476 41 155.63 136.491 106.4479 166.5341 0.1059 0.119 0.4543 0.5457 42 161.67 136.7099 105.9102 167.5097 0.0561 0.1143 0.2723 0.5501 43 163.51 136.8131 105.238 168.3883 0.0487 0.0614 0.3109 0.5514 44 162.91 136.6858 104.3351 169.0365 0.0561 0.0521 0.2224 0.5472 45 164.8 136.5553 103.4681 169.6425 0.0471 0.0592 0.1152 0.5431 46 164.98 136.6028 102.8163 170.3892 0.0499 0.0509 0.0961 0.5433 47 154.54 136.7218 102.2435 171.2001 0.1556 0.0541 0.0532 0.5451 48 148.6 136.7323 101.5571 171.9075 0.2542 0.1605 0.0706 0.5444 49 149.19 136.6443 100.7838 172.5048 0.2465 0.2567 0.1795 0.5417 50 150.61 136.6018 100.0818 173.1217 0.2261 0.2496 0.2197 0.54 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 23 0.0174 -0.0057 0 0.6079 0 0 24 0.0309 0.0133 0.0095 3.3928 2.0003 1.4143 25 0.0429 -0.0077 0.0089 1.1319 1.7109 1.308 26 0.0524 -0.0311 0.0145 17.8065 5.7348 2.3947 27 0.0573 -0.0492 0.0214 44.4428 13.4764 3.671 28 0.0612 -0.0228 0.0216 9.745 12.8545 3.5853 29 0.0663 0.0051 0.0193 0.4829 11.0871 3.3297 30 0.0726 0.0689 0.0255 88.7694 20.7974 4.5604 31 0.0776 0.0645 0.0298 76.98 27.0399 5.2 32 0.0811 0.0953 0.0363 168.5934 41.1953 6.4184 33 0.0844 0.1443 0.0462 391.0026 72.9959 8.5438 34 0.0885 0.1604 0.0557 483.5995 107.2129 10.3544 35 0.0929 0.2093 0.0675 816.8798 161.8026 12.7202 36 0.0965 0.197 0.0768 720.791 201.7304 14.2032 37 0.0994 0.1231 0.0798 283.0073 207.1488 14.3927 38 0.1024 0.1028 0.0813 198.2354 206.5918 14.3733 39 0.1059 0.1309 0.0842 320.8335 213.3119 14.6052 40 0.1094 0.1323 0.0869 326.3403 219.5912 14.8186 41 0.1123 0.1402 0.0897 366.302 227.3128 15.0769 42 0.1149 0.1826 0.0943 623.0045 247.0974 15.7193 43 0.1178 0.1951 0.0991 712.722 269.27 16.4094 44 0.1208 0.1919 0.1033 687.7073 288.2899 16.9791 45 0.1236 0.2068 0.1078 797.7632 310.4409 17.6193 46 0.1262 0.2077 0.112 805.2673 331.0587 18.195 47 0.1287 0.1303 0.1127 317.4874 330.5158 18.1801 48 0.1313 0.0868 0.1117 140.8427 323.2207 17.9783 49 0.1339 0.0918 0.111 157.3943 317.079 17.8067 50 0.1364 0.1025 0.1107 196.2309 312.763 17.6851

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260360819mkpgu5bh228lu4f/18gkv1260360651.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260360819mkpgu5bh228lu4f/18gkv1260360651.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260360819mkpgu5bh228lu4f/24vf81260360651.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260360819mkpgu5bh228lu4f/24vf81260360651.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) #cut off periods par1 <- 28 par2 <- as.numeric(par2) #lambda par3 <- as.numeric(par3) #degree of non-seasonal differencing par4 <- as.numeric(par4) #degree of seasonal differencing par5 <- as.numeric(par5) #seasonal period par6 <- as.numeric(par6) #p par6 <- 3 par7 <- as.numeric(par7) #q par7 <- 3 par8 <- as.numeric(par8) #P par9 <- as.numeric(par9) #Q if (par10 == 'TRUE') par10 <- TRUE if (par10 == 'FALSE') par10 <- FALSE if (par2 == 0) x <- log(x) if (par2 != 0) x <- x^par2 lx <- length(x) first <- lx - 2*par1 nx <- lx - par1 nx1 <- nx + 1 fx <- lx - nx if (fx < 1) { fx <- par5 nx1 <- lx + fx - 1 first <- lx - 2*fx } first <- 1 if (fx < 3) fx <- round(lx/10,0) (arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML')) (forecast <- predict(arima.out,par1)) (lb <- forecast$pred - 1.96 * forecast$se) (ub <- forecast$pred + 1.96 * forecast$se) if (par2 == 0) { x <- exp(x) forecast$pred <- exp(forecast$pred) lb <- exp(lb) ub <- exp(ub) } if (par2 != 0) { x <- x^(1/par2) forecast$pred <- forecast$pred^(1/par2) lb <- lb^(1/par2) ub <- ub^(1/par2) } if (par2 < 0) { olb <- lb lb <- ub ub <- olb } (actandfor <- c(x[1:nx], forecast$pred)) (perc.se <- (ub-forecast$pred)/1.96/forecast$pred) bitmap(file='test1.png') opar <- par(mar=c(4,4,2,2),las=1) ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub)) plot(x,ylim=ylim,type='n',xlim=c(first,lx)) usr <- par('usr') rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon') rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender') abline(h= (-3:3)*2 , col ='gray', lty =3) polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA) lines(nx1:lx, lb , lty=2) lines(nx1:lx, ub , lty=2) lines(x, lwd=2) lines(nx1:lx, forecast$pred , lwd=2 , col ='white') box() par(opar) dev.off() prob.dec <- array(NA, dim=fx) prob.sdec <- array(NA, dim=fx) prob.ldec <- array(NA, dim=fx) prob.pval <- array(NA, dim=fx) perf.pe <- array(0, dim=fx) perf.mape <- array(0, dim=fx) perf.mape1 <- array(0, dim=fx) perf.se <- array(0, dim=fx) perf.mse <- array(0, dim=fx) perf.mse1 <- array(0, dim=fx) perf.rmse <- array(0, dim=fx) for (i in 1:fx) { locSD <- (ub[i] - forecast$pred[i]) / 1.96 perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i] perf.se[i] = (x[nx+i] - forecast$pred[i])^2 prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD) prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD) prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD) prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD) } perf.mape[1] = abs(perf.pe[1]) perf.mse[1] = abs(perf.se[1]) for (i in 2:fx) { perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i]) perf.mape1[i] = perf.mape[i] / i perf.mse[i] = perf.mse[i-1] + perf.se[i] perf.mse1[i] = perf.mse[i] / i } perf.rmse = sqrt(perf.mse1) bitmap(file='test2.png') plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub))) dum <- forecast$pred dum[1:par1] <- x[(nx+1):lx] lines(dum, lty=1) lines(ub,lty=3) lines(lb,lty=3) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'time',1,header=TRUE) a<-table.element(a,'Y[t]',1,header=TRUE) a<-table.element(a,'F[t]',1,header=TRUE) a<-table.element(a,'95% LB',1,header=TRUE) a<-table.element(a,'95% UB',1,header=TRUE) a<-table.element(a,'p-value<br />(H0: Y[t] = F[t])',1,header=TRUE) a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE) a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE) mylab <- paste('P(F[t]>Y[',nx,sep='') mylab <- paste(mylab,'])',sep='') a<-table.element(a,mylab,1,header=TRUE) a<-table.row.end(a) for (i in (nx-par5):nx) { a<-table.row.start(a) a<-table.element(a,i,header=TRUE) a<-table.element(a,x[i]) a<-table.element(a,'-') a<-table.element(a,'-') a<-table.element(a,'-') a<-table.element(a,'-') a<-table.element(a,'-') a<-table.element(a,'-') a<-table.element(a,'-') a<-table.row.end(a) } for (i in 1:fx) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,round(x[nx+i],4)) a<-table.element(a,round(forecast$pred[i],4)) a<-table.element(a,round(lb[i],4)) a<-table.element(a,round(ub[i],4)) a<-table.element(a,round((1-prob.pval[i]),4)) a<-table.element(a,round((1-prob.dec[i]),4)) a<-table.element(a,round((1-prob.sdec[i]),4)) a<-table.element(a,round((1-prob.ldec[i]),4)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Univariate ARIMA Extrapolation Forecast Performance',7,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'time',1,header=TRUE) a<-table.element(a,'% S.E.',1,header=TRUE) a<-table.element(a,'PE',1,header=TRUE) a<-table.element(a,'MAPE',1,header=TRUE) a<-table.element(a,'Sq.E',1,header=TRUE) a<-table.element(a,'MSE',1,header=TRUE) a<-table.element(a,'RMSE',1,header=TRUE) a<-table.row.end(a) for (i in 1:fx) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,round(perc.se[i],4)) a<-table.element(a,round(perf.pe[i],4)) a<-table.element(a,round(perf.mape1[i],4)) a<-table.element(a,round(perf.se[i],4)) a<-table.element(a,round(perf.mse1[i],4)) a<-table.element(a,round(perf.rmse[i],4)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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